What is the integral from 0 to 2 of (x+2)-x^2 ?

The integral from 0 to 2 of (x+2)-x^2 is 10/3

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integral from 0 to 2 of (x+2)-x^2

\int_{0}^{2} (x + 2) - x^{2} d x

\frac{10}{3}

Decimal Notation

3.33333 \dots

Solution steps

\int_{0}^{2} x + 2 - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} x d x + \int_{0}^{2} 2 d x - \int_{0}^{2} x^{2} d x

\int_{0}^{2} x d x = 2

\int_{0}^{2} 2 d x = 4

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= 2 + 4 - \frac{8}{3}

Simplify

2 + 4 - \frac{8}{3} : \frac{10}{3}

= \frac{10}{3}

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What is the integral from 0 to 2 of (x+2)-x^2 ?
The integral from 0 to 2 of (x+2)-x^2 is 10/3